Problem: Simplify the following expression: $k = \dfrac{4g^2 + 4g}{4fg + 6hg} - \dfrac{g^2 - 5hg}{4fg + 6hg}$ You can assume $f,g,h \neq 0$.
Explanation: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{4g^2 + 4g - (g^2 - 5hg)}{4fg + 6hg}$ $k = \dfrac{3g^2 + 4g + 5hg}{4fg + 6hg}$ The numerator and denominator have a common factor of $g$, so we can simplify $k = \dfrac{3g + 4 + 5h}{4f + 6h}$